To avoid it happening, I'd just paint everything by hand and leave out the masking. I know that sounds like a wisecrack, but that's what I'd do.
Now, I do have a project on the bench that will involve using the airbrush, and so I will have to mask. I have a female figure in a dress uniform, and I want to give her stockings. I have to airbrush that to get it right. I plan on using plastic wrap, or cling film, I think the rest of the Anglosphere calls it. Saran Wrap. That uses static to adhere, rather than an adhesive. I think I read that tip in Andrea's "Painting Girls" book.
It's funny, but you can do everything right, and still have masking tape lift off paint. Repeat all of your steps, and it comes away clean.
Prost!
Brad